Make an object infinitely far away?
You could make the moon move relative to the camera.


Select the camera and &#8679; ShiftS snap the cursor to it. Then add an empty at that position. &#8679; ShiftA

Select the moon. &#8679; Shift select the the empty and parent the moon to the empty &#9096; CtrlP.

Select the empty. Add a Copy Location Constraint. Choose the camera as the target.  
Fake lighting by the moon with a sun lamp. The sun lamp type sends parallel rays, which simulate an object which is infinitely far away.
You may encounter that the moon is casting a shadow (from the sun light) or emitting light (if you're using the cycles render engine). To prevent that in cycles, you modify the moons visibility settings and disable all options except camera.

If you are using EEVEE, simply move the sun light between all object and the moon, which has to have the furthest distance to the camera.


Due to the relative offset, the moon is always at the same position.